A Liberal Democrat cabinet minister has widened an increasingly damaging rift inside the coalition by warning that the prime minister and other senior Conservatives could face legal action over the manner in which they have campaigned for a no vote in next week's referendum on a change to the voting system.

Chris Huhne, the Lib Dem energy secretary, admitted for the first time that the campaign against the alternative vote by senior Conservatives will make the coalition government "more difficult" to manage in the aftermath of the 5 May referendum.

Huhne said the claims made by David Cameron, George Osborne and other Tories undermined their credibility. He is concerned about two claims made by the Conservatives – that a move to AV will need new counting machines, and so cost as much as £250m, and that it will favour extremist parties. He said: "If they don't come clean on this, I am sure the law courts will."

"Australia's used [AV] for 80 years without ever using voting machines. If they can't substantiate that, there's simple legal redress. They had better come clean pretty fast."

Lib Dems have adopted an increasingly vituperative tone as they attempt to correct what they believe to be "untruths" pushed out by Tories and the no campaign and match the vigour with which the other side is campaigning. The Lib Dems had not expected senior Tories to take so active a role in the campaign, and only latterly decided to do the same for the yes campaign. Some of the strident language will also be an attempt to persuade their voters of their distance from the Conservatives in the hope of firming up support for a yes vote, as well as encouraging Labour supporters to come out and vote for reform.

In the Independent on Sunday, Nick Clegg, the Lib Dem leader and deputy prime minister, accused Cameron of "defending the indefensible", implying that he was part of "a rightwing clique who want to keep things the way they are". The no campaign were putting out "lies, misinformation and deceit", he said.

Huhne also wrote to Osborne, the chancellor, before the weekend, accusing him of lying about the cost of reforming the system and asking him to withdraw "falsehoods". But the threat of legal action would mean coalition relations remain uncomfortable long after the referendum has been decided.

Huhne told the BBC: "It is frankly worrying if you have colleagues, who you have respected and who you have worked well with, who are making claims which have no foundation in truth whatsoever. If they don't come clean on this, I am sure the law courts will.

"It is going to undermine the credibility of colleague ministers – the prime minister and the chancellor of the exchequer and the foreign secretary [William Hague] – if they use repeatedly allegations that have no foundation in truth whatsoever.

"That is not good for the coalition. We have a job to do in the coalition government to clean up the mess we have inherited at the time of the last election."

"It is going to be a lot more difficult if you don't have the same respect for colleagues because, frankly, they have departed so far from the foundations of truth in an election campaign."

The Lib Dem deputy leader, Simon Hughes, echoed Huhne's threat of action, telling the BBC that the Electoral Commission could be asked to investigate the no campaign and to ensure that future elections did not see "untrue statements in official campaigns circulated".

Hague struck a more measured tone, playing down the differences and insisting that the coalition was working well.

"We're used in general election campaigns to accusations flying back and forth and I think a lot of these accusations are directed at the no campaign rather than the Conservative party," he told the BBC's Andrew Marr Show.

"These things do get bandied about in a referendum campaign. Feelings run high, people get excited. I think the important thing for people to know is the coalition is working well together. It continues to work well together.

"Yes, we all have strong feelings about it and I very much hope people will vote no, but at the end of it the coalition will be working very well together."

Hague also dismissed the idea that Cameron will have to offer more concessions to Clegg in order to bolster the position of the Lib Dems in the coalition.

The foreign secretary said: "What we are doing in government is finding the right way forward together. It doesn't normally work in the manner of concessions to one side or the other."

Hughes said the Tory party co-chairman Lady Warsi had been "peddling untruths" that the British National party would gain in any move to AV. But Hague said: "I think she's right, because what do you do in a system where there are third and fourth preferences?

"Will the candidates in marginal seats have to think about how they're going to get the second, third and fourth preferences of people who have voted for the BNP?"

" These things are therefore not disputed facts, they're matters of opinion about the implication of AV and they should be understood as that."

He also said "there was no doubt" that having a more complicated system would cost more and that it was a legitimate issue to raise in a campaign.

Putting the case against AV, Hague said: "You can argue for a decisive system, which we have most of the time in this country, or you can argue for a proportional system as they have in Germany."

Cameron acknowledged last week that the referendum campaign, which lines up most of the Conservative party against the Liberal Democrats, had created a "choppy" period for the coalition.

A Guardian/ICM poll published last week suggested the no campaign had gone into a 16-point lead, by 58% to 42%.